risk management for mathematical optimization problems under uncertainty
In this paper we present a set of risk averse measures as alternatives to the objective function expected value (i.e. a so-called risk neutral environment) to optimize multistage mixed 0-1 linear optimization problems under uncertainty via scenario analysis. The risk averse measures to analyze whose validity is tested in this work are as follows: min-max regret, Conditional Value-at-Risk, two-stage and multistage mean-risk immunization, two-stage and multistage Value-at-Risk strategy, two-stage Conditional Value-at-Risk strategy, two-stage stochastic dominance strategy, and the new ones two-stage and multistage mixture of VaR & stochastic dominance. Most of these measures require from the modeller a threshold for the objective function related to each scenario (the recent ones even allow a set of so-called objective function profiles) and a failure probability for not reaching the threshold. We will analyze various application fields of risk management in economics, such as Air Traffic Flow Management, Revenue Management, Mining extraction planning, Rapid transit network designing, Production and Supply Chain Management, Natural gas and Oil infrastructure network designing, electricity power generation capacity expansion planning along a long term, and Immunization of fixed-income financial security portfolios. We will focus our analysis on the last one of the cited application fields.
| Departamento de Ingeniería Industrial |
| Facultad de Ciencias Físicas y Matemáticas | Universidad de Chile |
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